Around homogeneity

Abstract

Forty-five years ago, a young researcher in finite permutation group theory encountered a paper by Robert Woodrow. The homogeneous triangle-free graph Woodrow described there seemed to be an infinite analogue of the Higman--Sims graph which had played an important role in the researcher's thesis. The encounter changed the course of the researcher's career. This paper is the story of that event and its aftermath. The final section of the paper suggests that Fra\"{\i}ss\'e classes of rigid structures are a potentially interesting generalisation of Ramsey classes.